Waves and Optics - AQA A-Level Physics Notes (Flashcards)

Progressive waves

A progressive wave is a wave that transfers energy through a medium without transferring matter.
Wave speed relation: v = f \lambda (wave speed v is the product of frequency f and wavelength \lambda).
Displacement vs amplitude:
- Displacement: the distance from the equilibrium position at a given point on the wave.
- Amplitude: the maximum displacement from equilibrium.
Phase difference: the difference in the phase angle between two points on a wave; measured in degrees or radians.
Transverse vs longitudinal waves:
- Transverse: oscillations are perpendicular (\text{to the direction of energy transfer}).
- Longitudinal: oscillations are parallel (\text{to the direction of energy transfer}).
Examples:
- Transverse wave: light wave.
- Longitudinal wave: sound wave.
Law of reflection: the angle of incidence equals the angle of reflection, (\thetai = \thetar).
Snell’s Law: n1 \sin\theta1 = n2 \sin\theta2

When light enters a denser medium, it slows down and bends towards the normal (refraction).
Diffraction is most significant when the gap size is approximately equal to the wavelength.
Principle of superposition: the resultant displacement at a point is the vector sum of displacements from the individual waves.
Constructive interference:
- Waves are in phase and have a path difference of \Delta = n\lambda (where n is an integer).
Destructive interference:
- Waves are out of phase by (\pi) (180°) and have a path difference of \Delta = (n + \tfrac{1}{2})\lambda.
Coherence:
- Two wave sources are coherent if they have a constant phase difference and the same frequency.
Stationary (standing) wave:
- Formed by the superposition of two progressive waves with the same frequency and amplitude moving in opposite directions.
Nodes and antinodes:
- Nodes: points of zero amplitude.
- Antinodes: points of maximum amplitude.
First harmonic (fundamental) on a stretched string:
- The lowest frequency standing wave with one antinode and two nodes; L = \tfrac{\lambda}{2}, so \lambda = 2L.
- For the fundamental, the string supports the mode where half a wavelength fits into the length of the string.

Absolute refractive index: n = \frac{c}{v}
- c: speed of light in vacuum; v: speed of light in the medium.
Critical angle: \sin\thetac = \frac{n2}{n_1}
Total internal reflection requires:
- Light travels from a more dense medium to a less dense medium.
- The angle of incidence exceeds the critical angle ((\thetai > \thetac)).

Fringe spacing in Young’s double-slit experiment:
- w = \dfrac{\lambda D}{s}
- where (D) is the distance to the screen and (s) is the separation between slits.
Bright fringe: constructive interference (waves arrive in phase).
Dark fringe: destructive interference (waves arrive out of phase by (\pi) radians).
Diffraction grating equation:
- n \lambda = d \sin\theta
- n is the order of the fringe, (d) is the slit spacing, and (\theta) is the angle of diffraction.
Effect of increasing the number of slits in a diffraction grating:
- Produces sharper and more widely spaced maxima in the interference pattern.

Wave behavior is governed by superposition, energy transport without matter movement, and boundary conditions at interfaces (refraction, reflection).
Coherence is essential for stable interference patterns; practical sources include lasers (high coherence).
Understanding standing waves underpins musical instruments, sensors, and engineering of strings and membranes.
Refractive index and critical angle underpin fiber optics, endoscopy, and optical communication technologies.
Diffraction and interference principles explain imaging resolution limits and the design of optical gratings used in spectroscopy.
Practical considerations:
- In optical design, controlling coherence and wavelength allows precise control over interference patterns for filtering and wavelength-selective devices.
- Total internal reflection enables efficient light guidance in optical fibers, critical for modern communications.
Philosophical/practical implications:
- Wave-particle duality considerations arise when interpreting interference phenomena with photons and electrons; these principles reinforce the wave nature of light and matter in physics curricula.